Subgroups — C₇×#24328 #13201544

Order 1792.

1070 conjugacy classes of subgroups.

The subgroup lattice has 524 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×#557	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₇×#474	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄×C₇×SD₁₆	C₂	1	1	yes	maximal, characteristic
4	C₇×#2538	C₂	1	1	yes	maximal, characteristic
5	C₇×#2059	C₂	1	2	yes	maximal, complemented
6	C₇×#2025	C₂	1	2	yes	maximal
7	C₇×#1990	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇×#1984	C₂	1	1	yes	maximal, characteristic, complemented
9	C₇×#1880	C₂	1	2	yes	maximal
10	C₇×#1863	C₂	1	2	yes	maximal, complemented
11	C₇×#1803	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×C₇×SD₁₆	C₂²	1	1	yes	characteristic
13	C₇×#557	—	2	4	no	—
14	C₇×#557	—	2	4	no	—
15	C₂×C₇×C₄⋊Q₈	—	2	1	no	—
16	C₂×C₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic
17	C₂×C₇×#125	—	2	2	no	—
18	C₂×C₇×#125	C₂²	1	2	yes	—
19	C₂×C₇×C₂²⋊Q₈	—	2	1	no	—
20	C₂×C₄×C₇×Q₈	—	2	1	no	—
21	C₂×C₄×C₇×Q₈	C₂²	1	2	yes	—
22	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic
23	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic
24	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
25	C₇×#474	—	2	4	no	—
26	C₄×C₇×SD₁₆	—	2	4	no	—
27	C₂×C₇×#107	C₂²	1	2	yes	—
28	C₂×C₇×#106	C₂²	1	1	yes	characteristic
29	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
30	C₂×C₇×#103	C₂²	1	1	yes	characteristic
31	C₂×C₇×#103	C₂²	1	2	yes	—
32	C₂×C₇×#102	C₂²	1	1	yes	characteristic
33	C₂×C₇×#102	C₂²	1	2	yes	—
34	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
35	C₇×#396	—	2	2	no	—
36	C₇×#390	C₂²	1	2	yes	—
37	C₇×#389	C₂²	1	2	yes	—
38	C₇×#384	C₂²	1	1	yes	characteristic
39	C₇×#380	—	2	1	no	—
40	C₇×#340	C₂²	1	2	yes	—
41	C₇×#340	C₂²	1	2	yes	—
42	C₇×#340	C₂²	1	2	yes	—
43	C₇×#336	C₂²	1	2	yes	—
44	C₇×#336	C₂²	1	2	yes	—
45	#24328	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
46	C₂²×C₇×Q₈	—	2	1	no	—
47	C₂²×C₇×Q₈	D₄	1	1	yes	characteristic
48	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
49	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
50	C₂³×C₄×C₇	—	2	1	no	—
51	C₂×C₇×SD₁₆	—	2	2	no	—
52	C₂×C₇×SD₁₆	—	2	2	no	—
53	C₂×C₇×SD₁₆	Q₈	1	4	yes	complemented
54	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
55	C₂²×C₇×C₈	C₂³	1	2	yes	—
56	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
57	C₇×C₄⋊Q₈	—	2	8	no	—
58	C₇×C₄⋊Q₈	—	2	2	no	—
59	C₇×C₄⋊Q₈	D₄	1	4	yes	—
60	C₇×#125	—	2	16	no	—
61	C₇×#125	—	2	4	no	—
62	C₇×#125	—	2	4	no	—
63	C₇×C₂²⋊Q₈	—	4	4	no	—
64	C₄×C₇×Q₈	—	2	8	no	—
65	C₄×C₇×Q₈	—	2	4	no	—
66	C₄×C₇×Q₈	—	2	4	no	—
67	C₄×C₇×Q₈	—	2	2	no	—
68	C₄×C₇×Q₈	—	2	2	no	—
69	C₄×C₇×Q₈	—	2	2	no	—
70	C₄×C₇×Q₈	D₄	1	4	yes	—
71	C₄×C₇×D₄	—	2	2	no	—
72	C₄×C₇×D₄	—	2	2	no	—
73	C₂×C₇×C₄⋊C₄	—	2	2	no	—
74	C₂×C₇×C₄⋊C₄	—	2	1	no	—
75	C₂×C₇×C₄⋊C₄	—	2	2	no	—
76	C₂×C₇×C₄⋊C₄	—	2	1	no	—
77	C₂×C₇×C₄⋊C₄	—	2	2	no	—
78	C₂×C₇×C₄⋊C₄	—	2	1	no	—
79	C₂×C₇×C₄⋊C₄	—	2	2	no	—
80	C₂×C₇×C₄⋊C₄	—	2	1	no	—
81	C₂×C₇×C₄⋊C₄	D₄	1	1	yes	characteristic
82	C₂×C₇×C₄⋊C₄	D₄	1	2	yes	—
83	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
84	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
85	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
86	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
87	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
88	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
89	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
90	C₂×C₄²×C₇	—	2	2	no	—
91	C₂×C₄²×C₇	—	2	1	no	—
92	C₂×C₄²×C₇	C₂³	1	2	yes	—
93	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
94	C₇×#107	—	2	4	no	—
95	C₇×#106	—	2	2	no	—
96	C₇×C₄⋊C₈	—	2	2	no	—
97	C₇×#103	—	2	2	no	—
98	C₇×#103	—	2	4	no	—
99	C₇×#102	—	2	4	no	—
100	C₇×#102	—	2	2	no	—
101	C₄×C₇×C₈	—	2	2	no	—
102	C₇×#95	—	2	2	no	—
103	C₂×#557	C₂×C₇	1	1	yes	characteristic, complemented
104	C₂×#474	C₂×C₇	1	1	yes	characteristic
105	C₂×C₄×SD₁₆	C₂×C₇	1	1	yes	characteristic
106	#2538	C₂×C₇	1	1	yes	characteristic
107	#2059	C₂×C₇	1	2	yes	complemented
108	#2025	C₂×C₇	1	2	yes	—
109	#1990	C₂×C₇	1	1	yes	characteristic, complemented
110	#1984	C₂×C₇	1	1	yes	characteristic, complemented
111	#1880	C₂×C₇	1	2	yes	—
112	#1863	C₂×C₇	1	2	yes	complemented
113	#1803	C₂×C₇	1	1	yes	characteristic, complemented
114	C₂⁴×C₇	—	2	1	no	—
115	C₂×C₇×Q₈	—	2	2	no	—
116	C₂×C₇×Q₈	—	2	4	no	—
117	C₂×C₇×Q₈	—	2	2	no	—
118	C₂×C₇×Q₈	—	2	2	no	—
119	C₂×C₇×Q₈	—	2	1	no	—
120	C₂×C₇×Q₈	—	2	1	no	—
121	C₂×C₇×Q₈	—	2	1	no	—
122	C₂×C₇×Q₈	—	4	2	no	—
123	C₂×C₇×Q₈	—	4	2	no	—
124	C₂×C₇×Q₈	C₂×D₄	1	2	yes	—
125	C₂×C₇×Q₈	C₂×Q₈	1	2	yes	—
126	C₂×C₇×Q₈	#41	1	2	yes	—
127	C₂×C₇×D₄	—	2	1	no	—
128	C₂×C₇×D₄	—	2	1	no	—
129	C₂×C₇×D₄	—	2	1	no	—
130	C₂×C₇×D₄	—	2	1	no	—
131	C₂×C₇×D₄	—	2	1	no	—
132	C₂×C₇×D₄	C₂×Q₈	1	2	yes	—
133	C₂²×C₄×C₇	—	2	1	no	—
134	C₂²×C₄×C₇	—	2	1	no	—
135	C₂²×C₄×C₇	—	2	2	no	—
136	C₂²×C₄×C₇	—	2	1	no	—
137	C₂²×C₄×C₇	—	2	2	no	—
138	C₂²×C₄×C₇	—	4	2	no	—
139	C₂²×C₄×C₇	—	4	2	no	—
140	C₂²×C₄×C₇	—	4	2	no	—
141	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
142	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
143	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
144	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
145	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
146	C₇×SD₁₆	—	2	8	no	—
147	C₂×C₇×C₈	—	2	1	no	—
148	C₂×C₇×C₈	—	2	1	no	—
149	C₂×C₇×C₈	—	2	1	no	—
150	C₂×C₇×C₈	—	2	2	no	—
151	C₂×C₇×C₈	—	2	2	no	—
152	C₂×C₇×C₈	—	2	1	no	—
153	C₂×C₇×C₈	—	2	1	no	—
154	C₂×C₇×C₈	—	2	2	no	—
155	C₂×C₇×C₈	C₂×Q₈	1	2	yes	—
156	C₇×C₄⋊C₄	—	2	8	no	—
157	C₇×C₄⋊C₄	—	2	8	no	—
158	C₇×C₄⋊C₄	—	2	8	no	—
159	C₇×C₄⋊C₄	—	2	4	no	—
160	C₇×C₄⋊C₄	—	2	4	no	—
161	C₇×C₄⋊C₄	—	2	2	no	—
162	C₇×C₄⋊C₄	—	2	4	no	—
163	C₇×C₄⋊C₄	—	2	1	no	—
164	C₇×C₄⋊C₄	—	2	2	no	—
165	C₇×C₄⋊C₄	—	2	1	no	—
166	C₇×C₄⋊C₄	—	2	1	no	—
167	C₇×C₄⋊C₄	—	2	2	no	—
168	C₇×C₄⋊C₄	—	2	2	no	—
169	C₇×C₄⋊C₄	—	4	4	no	—
170	C₇×C₄⋊C₄	—	4	2	no	—
171	C₇×C₄⋊C₄	—	8	1	no	—
172	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
173	C₇×C₄⋊C₄	C₂×D₄	1	4	yes	—
174	C₇×C₂²⋊C₄	—	4	4	no	—
175	C₇×C₂²⋊C₄	—	4	2	no	—
176	C₇×C₂²⋊C₄	—	8	2	no	—
177	C₄²×C₇	—	2	8	no	—
178	C₄²×C₇	—	2	4	no	—
179	C₄²×C₇	—	2	2	no	—
180	C₄²×C₇	—	2	2	no	—
181	C₄²×C₇	C₂×D₄	1	2	yes	—
182	C₄²×C₇	C₂×D₄	1	2	yes	—
183	C₂²×SD₁₆	C₂²×C₇	1	1	yes	characteristic
184	#557	—	2	4	no	—
185	#557	—	2	4	no	—
186	C₂×C₄⋊Q₈	—	2	1	no	—
187	C₂×C₄⋊Q₈	C₂²×C₇	1	1	yes	characteristic
188	C₂×#125	—	2	2	no	—
189	C₂×#125	C₂²×C₇	1	2	yes	—
190	C₂×C₂²⋊Q₈	—	2	1	no	—
191	C₂×C₄×Q₈	—	2	1	no	—
192	C₂×C₄×Q₈	C₂²×C₇	1	2	yes	—
193	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic
194	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic
195	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
196	#474	—	2	4	no	—
197	C₄×SD₁₆	—	2	4	no	—
198	C₂×#107	C₂²×C₇	1	2	yes	—
199	C₂×#106	C₂²×C₇	1	1	yes	characteristic
200	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
201	C₂×#103	C₂²×C₇	1	2	yes	—
202	C₂×#103	C₂²×C₇	1	1	yes	characteristic
203	C₂×#102	C₂²×C₇	1	2	yes	—
204	C₂×#102	C₂²×C₇	1	1	yes	characteristic
205	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
206	#396	—	2	2	no	—
207	#390	C₂²×C₇	1	2	yes	—
208	#389	C₂²×C₇	1	2	yes	—
209	#384	C₂²×C₇	1	1	yes	characteristic
210	#380	—	2	1	no	—
211	#340	C₂²×C₇	1	2	yes	—
212	#340	C₂²×C₇	1	2	yes	—
213	#340	C₂²×C₇	1	2	yes	—
214	#336	C₂²×C₇	1	2	yes	—
215	#336	C₂²×C₇	1	2	yes	—
216	C₂³×C₇	—	2	2	no	—
217	C₂³×C₇	—	4	1	no	—
218	C₂³×C₇	—	4	1	no	—
219	C₂³×C₇	—	4	1	no	—
220	C₂³×C₇	—	4	1	no	—
221	C₂³×C₇	—	4	1	no	—
222	C₂³×C₇	—	4	1	no	—
223	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
224	C₇×Q₈	—	2	2	no	—
225	C₇×Q₈	—	2	2	no	—
226	C₇×Q₈	—	2	2	no	—
227	C₇×Q₈	—	4	4	no	—
228	C₇×Q₈	—	4	8	no	—
229	C₇×Q₈	C₂²⋊Q₈	1	4	yes	complemented
230	C₇×D₄	—	2	2	no	—
231	C₇×D₄	—	2	2	no	—
232	C₇×D₄	—	4	1	no	—
233	C₇×D₄	—	4	1	no	—
234	C₂×C₄×C₇	—	2	2	no	—
235	C₂×C₄×C₇	—	2	2	no	—
236	C₂×C₄×C₇	—	2	2	no	—
237	C₂×C₄×C₇	—	2	1	no	—
238	C₂×C₄×C₇	—	2	1	no	—
239	C₂×C₄×C₇	—	2	2	no	—
240	C₂×C₄×C₇	—	2	2	no	—
241	C₂×C₄×C₇	—	2	2	no	—
242	C₂×C₄×C₇	—	2	4	no	—
243	C₂×C₄×C₇	—	2	2	no	—
244	C₂×C₄×C₇	—	2	2	no	—
245	C₂×C₄×C₇	—	2	2	no	—
246	C₂×C₄×C₇	—	2	2	no	—
247	C₂×C₄×C₇	—	4	2	no	—
248	C₂×C₄×C₇	—	4	2	no	—
249	C₂×C₄×C₇	—	4	1	no	—
250	C₂×C₄×C₇	—	4	1	no	—
251	C₂×C₄×C₇	—	4	1	no	—
252	C₂×C₄×C₇	—	4	2	no	—
253	C₂×C₄×C₇	—	4	1	no	—
254	C₂×C₄×C₇	—	4	2	no	—
255	C₂×C₄×C₇	—	4	1	no	—
256	C₂×C₄×C₇	—	4	2	no	—
257	C₂×C₄×C₇	—	8	4	no	—
258	C₂×C₄×C₇	#120	1	2	yes	—
259	C₂×C₄×C₇	#120	1	2	yes	—
260	C₂×C₄×C₇	#135	1	2	yes	—
261	C₂×C₄×C₇	AGL(1,ℤ/8)	1	2	yes	—
262	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
263	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
264	C₂×C₄×C₇	C₂²×Q₈	1	1	yes	characteristic
265	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
266	C₂×C₄×C₇	2₋¹⁺⁴	1	1	yes	characteristic
267	C₂×C₄×C₇	2₋¹⁺⁴	1	1	yes	characteristic
268	C₇×C₈	—	2	2	no	—
269	C₇×C₈	—	4	1	no	—
270	C₇×C₈	—	4	2	no	—
271	C₂²×Q₈	—	2	1	no	—
272	C₂²×Q₈	C₇×D₄	1	1	yes	characteristic
273	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
274	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
275	C₂³×C₄	—	2	1	no	—
276	C₂×SD₁₆	—	2	2	no	—
277	C₂×SD₁₆	—	2	2	no	—
278	C₂×SD₁₆	C₇×Q₈	1	4	yes	complemented
279	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
280	C₂²×C₈	C₂³×C₇	1	2	yes	—
281	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
282	C₄⋊Q₈	—	2	8	no	—
283	C₄⋊Q₈	—	2	2	no	—
284	C₄⋊Q₈	C₇×D₄	1	4	yes	—
285	#125	—	2	16	no	—
286	#125	—	2	4	no	—
287	#125	—	2	4	no	—
288	C₂²⋊Q₈	—	4	4	no	—
289	C₄×Q₈	—	2	8	no	—
290	C₄×Q₈	—	2	4	no	—
291	C₄×Q₈	—	2	4	no	—
292	C₄×Q₈	—	2	2	no	—
293	C₄×Q₈	—	2	2	no	—
294	C₄×Q₈	—	2	2	no	—
295	C₄×Q₈	C₇×D₄	1	4	yes	—
296	C₄×D₄	—	2	2	no	—
297	C₄×D₄	—	2	2	no	—
298	C₂×C₄⋊C₄	—	2	2	no	—
299	C₂×C₄⋊C₄	—	2	1	no	—
300	C₂×C₄⋊C₄	—	2	2	no	—
301	C₂×C₄⋊C₄	—	2	1	no	—
302	C₂×C₄⋊C₄	—	2	2	no	—
303	C₂×C₄⋊C₄	—	2	1	no	—
304	C₂×C₄⋊C₄	—	2	2	no	—
305	C₂×C₄⋊C₄	—	2	1	no	—
306	C₂×C₄⋊C₄	C₇×D₄	1	1	yes	characteristic
307	C₂×C₄⋊C₄	C₇×D₄	1	2	yes	—
308	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
309	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
310	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
311	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
312	C₂×C₂²⋊C₄	—	2	1	no	—
313	C₂×C₂²⋊C₄	—	2	2	no	—
314	C₂×C₂²⋊C₄	—	2	2	no	—
315	C₂×C₄²	—	2	2	no	—
316	C₂×C₄²	—	2	1	no	—
317	C₂×C₄²	C₂³×C₇	1	2	yes	—
318	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
319	#107	—	2	4	no	—
320	#106	—	2	2	no	—
321	C₄⋊C₈	—	2	2	no	—
322	#103	—	2	2	no	—
323	#103	—	2	4	no	—
324	#102	—	2	2	no	—
325	#102	—	2	4	no	—
326	C₄×C₈	—	2	2	no	—
327	#95	—	2	2	no	—
328	C₂²×C₇	—	4	2	no	—
329	C₂²×C₇	—	4	2	no	—
330	C₂²×C₇	—	4	2	no	—
331	C₂²×C₇	—	8	1	no	—
332	C₂²×C₇	—	8	1	no	—
333	C₂²×C₇	—	8	1	no	—
334	C₂²×C₇	—	8	1	no	—
335	C₂²×C₇	C₂×#120	1	1	yes	characteristic
336	C₂²×C₇	#548	1	1	yes	characteristic
337	C₂²×C₇	D₄×Q₈	1	1	yes	characteristic
338	C₂²×C₇	C₂×#135	1	1	yes	characteristic
339	C₂²×C₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
340	C₂²×C₇	#577	1	1	yes	characteristic
341	C₂²×C₇	#578	1	1	yes	characteristic
342	C₄×C₇	—	2	4	no	—
343	C₄×C₇	—	2	2	no	—
344	C₄×C₇	—	4	2	no	—
345	C₄×C₇	—	4	4	no	—
346	C₄×C₇	—	4	2	no	—
347	C₄×C₇	—	4	2	no	—
348	C₄×C₇	—	8	2	no	—
349	C₄×C₇	—	8	1	no	—
350	C₄×C₇	#449	1	4	yes	—
351	C₄×C₇	C₂×C₂²⋊Q₈	1	1	yes	characteristic
352	C₄×C₇	#536	1	1	yes	characteristic
353	C₄×C₇	#548	1	1	yes	characteristic
354	C₄×C₇	D₄×Q₈	1	1	yes	characteristic
355	C₂⁴	—	2	1	no	—
356	C₂×Q₈	—	2	2	no	—
357	C₂×Q₈	—	2	4	no	—
358	C₂×Q₈	—	2	2	no	—
359	C₂×Q₈	—	2	2	no	—
360	C₂×Q₈	—	2	1	no	—
361	C₂×Q₈	—	2	1	no	—
362	C₂×Q₈	—	2	1	no	—
363	C₂×Q₈	—	4	2	no	—
364	C₂×Q₈	—	4	2	no	—
365	C₂×Q₈	C₂×C₇×D₄	1	2	yes	—
366	C₂×Q₈	C₂×C₇×Q₈	1	2	yes	—
367	C₂×Q₈	C₇×#41	1	2	yes	—
368	C₂×D₄	—	2	1	no	—
369	C₂×D₄	—	2	1	no	—
370	C₂×D₄	—	2	1	no	—
371	C₂×D₄	—	2	1	no	—
372	C₂×D₄	—	2	1	no	—
373	C₂×D₄	C₂×C₇×Q₈	1	2	yes	—
374	C₂²×C₄	—	2	1	no	—
375	C₂²×C₄	—	2	1	no	—
376	C₂²×C₄	—	2	2	no	—
377	C₂²×C₄	—	2	1	no	—
378	C₂²×C₄	—	2	2	no	—
379	C₂²×C₄	—	4	2	no	—
380	C₂²×C₄	—	4	2	no	—
381	C₂²×C₄	—	4	2	no	—
382	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
383	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
384	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
385	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
386	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
387	SD₁₆	—	2	8	no	—
388	C₂×C₈	—	2	1	no	—
389	C₂×C₈	—	2	1	no	—
390	C₂×C₈	—	2	1	no	—
391	C₂×C₈	—	2	2	no	—
392	C₂×C₈	—	2	2	no	—
393	C₂×C₈	—	2	1	no	—
394	C₂×C₈	—	2	1	no	—
395	C₂×C₈	—	2	2	no	—
396	C₂×C₈	C₂×C₇×Q₈	1	2	yes	—
397	C₄⋊C₄	—	2	8	no	—
398	C₄⋊C₄	—	2	8	no	—
399	C₄⋊C₄	—	2	8	no	—
400	C₄⋊C₄	—	2	4	no	—
401	C₄⋊C₄	—	2	4	no	—
402	C₄⋊C₄	—	2	2	no	—
403	C₄⋊C₄	—	2	4	no	—
404	C₄⋊C₄	—	2	1	no	—
405	C₄⋊C₄	—	2	2	no	—
406	C₄⋊C₄	—	2	1	no	—
407	C₄⋊C₄	—	2	1	no	—
408	C₄⋊C₄	—	2	2	no	—
409	C₄⋊C₄	—	2	2	no	—
410	C₄⋊C₄	—	4	4	no	—
411	C₄⋊C₄	—	4	2	no	—
412	C₄⋊C₄	—	8	1	no	—
413	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
414	C₄⋊C₄	C₂×C₇×D₄	1	4	yes	—
415	C₂²⋊C₄	—	4	4	no	—
416	C₂²⋊C₄	—	4	2	no	—
417	C₂²⋊C₄	—	8	2	no	—
418	C₄²	—	2	8	no	—
419	C₄²	—	2	4	no	—
420	C₄²	—	2	2	no	—
421	C₄²	—	2	2	no	—
422	C₄²	C₂×C₇×D₄	1	2	yes	—
423	C₄²	C₂×C₇×D₄	1	2	yes	—
424	C₂×C₇	—	8	2	no	—
425	C₂×C₇	#2409	1	1	yes	characteristic
426	C₂×C₇	C₂×#449	1	1	yes	characteristic
427	C₂×C₇	#3013	1	1	yes	characteristic
428	C₂×C₇	#3364	1	1	yes	characteristic
429	C₂×C₇	#3368	1	1	yes	characteristic
430	C₂×C₇	#3381	1	1	yes	characteristic
431	C₂×C₇	#3386	1	1	yes	characteristic
432	C₂³	—	2	2	no	—
433	C₂³	—	4	1	no	—
434	C₂³	—	4	1	no	—
435	C₂³	—	4	1	no	—
436	C₂³	—	4	1	no	—
437	C₂³	—	4	1	no	—
438	C₂³	—	4	1	no	—
439	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
440	Q₈	—	2	2	no	—
441	Q₈	—	2	2	no	—
442	Q₈	—	2	2	no	—
443	Q₈	—	4	4	no	—
444	Q₈	—	4	8	no	—
445	Q₈	C₇×C₂²⋊Q₈	1	4	yes	complemented
446	D₄	—	2	2	no	—
447	D₄	—	2	2	no	—
448	D₄	—	4	1	no	—
449	D₄	—	4	1	no	—
450	C₂×C₄	—	2	2	no	—
451	C₂×C₄	—	2	2	no	—
452	C₂×C₄	—	2	2	no	—
453	C₂×C₄	—	2	1	no	—
454	C₂×C₄	—	2	1	no	—
455	C₂×C₄	—	2	2	no	—
456	C₂×C₄	—	2	2	no	—
457	C₂×C₄	—	2	2	no	—
458	C₂×C₄	—	2	4	no	—
459	C₂×C₄	—	2	2	no	—
460	C₂×C₄	—	2	2	no	—
461	C₂×C₄	—	2	2	no	—
462	C₂×C₄	—	2	2	no	—
463	C₂×C₄	—	4	2	no	—
464	C₂×C₄	—	4	2	no	—
465	C₂×C₄	—	4	1	no	—
466	C₂×C₄	—	4	1	no	—
467	C₂×C₄	—	4	1	no	—
468	C₂×C₄	—	4	2	no	—
469	C₂×C₄	—	4	1	no	—
470	C₂×C₄	—	4	2	no	—
471	C₂×C₄	—	4	1	no	—
472	C₂×C₄	—	4	2	no	—
473	C₂×C₄	—	8	4	no	—
474	C₂×C₄	C₇×#120	1	2	yes	—
475	C₂×C₄	C₇×#120	1	2	yes	—
476	C₂×C₄	C₇×#135	1	2	yes	—
477	C₂×C₄	C₇×AGL(1,ℤ/8)	1	2	yes	—
478	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
479	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
480	C₂×C₄	C₂²×C₇×Q₈	1	1	yes	characteristic
481	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
482	C₂×C₄	C₇×2₋¹⁺⁴	1	1	yes	characteristic
483	C₂×C₄	C₇×2₋¹⁺⁴	1	1	yes	characteristic
484	C₈	—	2	2	no	—
485	C₈	—	4	1	no	—
486	C₈	—	4	2	no	—
487	C₇	#24328	1	1	yes	characteristic, direct product factor, Sylow
488	C₂²	—	4	2	no	—
489	C₂²	—	4	2	no	—
490	C₂²	—	4	2	no	—
491	C₂²	—	8	1	no	—
492	C₂²	—	8	1	no	—
493	C₂²	—	8	1	no	—
494	C₂²	—	8	1	no	—
495	C₂²	C₂×C₇×#120	1	1	yes	characteristic
496	C₂²	C₇×#548	1	1	yes	characteristic
497	C₂²	C₇×D₄×Q₈	1	1	yes	characteristic
498	C₂²	C₂×C₇×#135	1	1	yes	characteristic
499	C₂²	C₂×C₇×AGL(1,ℤ/8)	1	1	yes	characteristic
500	C₂²	C₇×#577	1	1	yes	characteristic
501	C₂²	C₇×#578	1	1	yes	characteristic
502	C₄	—	2	4	no	—
503	C₄	—	2	2	no	—
504	C₄	—	4	2	no	—
505	C₄	—	4	4	no	—
506	C₄	—	4	2	no	—
507	C₄	—	4	2	no	—
508	C₄	—	8	1	no	—
509	C₄	—	8	2	no	—
510	C₄	C₇×#449	1	4	yes	—
511	C₄	C₂×C₇×C₂²⋊Q₈	1	1	yes	characteristic
512	C₄	C₇×#536	1	1	yes	characteristic
513	C₄	C₇×#548	1	1	yes	characteristic
514	C₄	C₇×D₄×Q₈	1	1	yes	characteristic
515	C₂	—	8	2	no	—
516	C₂	C₇×#2409	1	1	yes	characteristic
517	C₂	C₂×C₇×#449	1	1	yes	characteristic
518	C₂	C₇×#3013	1	1	yes	characteristic
519	C₂	C₇×#3364	1	1	yes	characteristic
520	C₂	C₇×#3368	1	1	yes	characteristic
521	C₂	C₇×#3381	1	1	yes	characteristic
522	C₂	C₇×#3386	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₇	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₇
prime radical	C₂²×C₇×D₄	C₂³
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₇ ◁ C₂×C₄×C₇×Q₈ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₂×C₇×#557	C₂	semidirect
5. C₇×#2059	C₂	semidirect
7. C₇×#1990	C₂	semidirect
8. C₇×#1984	C₂	semidirect
10. C₇×#1863	C₂	semidirect
11. C₇×#1803	C₂	semidirect
45. #24328	C₇	direct (N × H)
53. C₂×C₇×SD₁₆	Q₈	semidirect
103. C₂×#557	C₂×C₇	semidirect
107. #2059	C₂×C₇	semidirect
109. #1990	C₂×C₇	semidirect
110. #1984	C₂×C₇	semidirect
112. #1863	C₂×C₇	semidirect
113. #1803	C₂×C₇	semidirect
229. C₇×Q₈	C₂²⋊Q₈	semidirect
278. C₂×SD₁₆	C₇×Q₈	semidirect
445. Q₈	C₇×C₂²⋊Q₈	semidirect
487. C₇	#24328	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₇×#557	2
C₂×C₇×#474	2
C₂×C₄×C₇×SD₁₆	2
C₇×#2538	2
C₇×#2059	2
C₇×#2025	2
C₇×#1990	2
C₇×#1984	2
C₇×#1880	2
C₇×#1863	2
C₇×#1803	2
#24328	7

Subgroups — C7×#24328 #13201544

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#24328 #13201544